Theorems on products of EPr matrices, II

Insolubility Theorems and EPR Argument

I present a very general and simple argument — based on the no-signalling theorem — showing that within the framework of the unitary Schrödinger equation it is impossible to reproduce the phenomenological description of quantum mechanical measurements (in particular the collapse of the state of the measured system) by assuming a suitable mixed initial state of the apparatus. The thrust of the a...

Theorems and counterexamples on structured matrices

On Family Rigidity Theorems II

In [LM], we proved a family version of the famous Witten rigidity theorems and several family vanishing theorems for elliptic genera. In this paper, we gerenalize our theorems [LM] in two directions. First we establish a family rigidity theorem for the Dirac operator on loop space twisted by general positive energy loop group representations. Second we prove a family rigidity theorem for spin-m...

On Random Matrices Ii

On the Infinite Products of Matrices

In different fields in space researches, Scientists are in need to deal with the product of matrices. In this paper, we develop conditions under which a product  of matrices chosen from a possibly infinite set of matrices 0 i i P    , j  M P j J     k i P   0 k k i  converges. There exists a vector norm such that all matrices in M are no expansive with respect to this norm and also ...